w.L. MASTERTON A N I ROBERTs.SCHWARPZ
1546
The Activity Coefficient of Trinitrotriamminecobalt(111) in Aqueous Salt Solutions
by W. L. Masterton and Robert N. Schwartz' The University of Connecticut, Storrs, Connecticut
(Received October 19, 1964)
Activity coefficients of Co(NH3)3(N02)3 in solutions of nine different alkali halides have been determined a t 25" from solubility measurements. With all but one of the salts studied, salting-in is observed, corresponding to activity coefficients less than unity. Setschenow parameters for the various salts fit an equation containing a constant salting-in term associated with dispersion forces and an electrostatic salting-out term whose magnitude varies inversely with ionic size.
Introduction As part of a general study of the thermodynamic properties of aqueous solutions of complex ion electrolytes,2 it seemed desirable to investigate the effect of added salts on the activity coefficient of a neutral complex. The compound chosen was trinitrotriamminecobalt(III), which is known to be relatively insoluble in water (0.0081 mole/l. a t 25") and stable to aquation. Activity coefficients, determined from solubility measurements, are discussed below in terms of the various 1 heories of salt effects. Studies of salt effectsd have been confined for the most part to organic molecules such as benzene and its derivatives or small inorganic molecules such as carbon dioxide and ammonia. The only work involving a coordination complex as the nonelectrolyte is that of Brfinsted and c o - ~ o r k e r s . ~The results of this study agree qualitatively with those of Brfinsted.
extracted with a small volume of cold water. The impurity, presumed to be [ C O N H ~ ) ~ ( X O ~ ) ~passed ]CI, into solution, leaving a residue of very low conductivity ( p = 4). Anal. Calcd. for CO("3)3(So2)3: NH3, 20.60. Found: NH3,20.61. Solubilities. Solubilities a t 25" were determined from optical density measurements carried out with a Rlodel DU Beckman spectrophotometer, using the broad absorption peak a t 435 nip. A calibration curve was established from readings on a series of solutions prepared by dissolving a known weight of C O ( S H ~ ) ~ (N02)3 in water. It was found that Beer's law was obeyed in the concentration range 6 x lop4 to 1 X M (O.D. = 0.185-0.310). All solutions obtained in the solubility measurements were diluted to fall in this range. The solubility of C O ( K H ~ ) ~ ( SinOpure ~ ) ~ water was determined by mechanically shaking excess solid with about 5 nil. of water in a sealed vial ininiersed in a constant temperature bath. A sample was withdrawn in a calibrated 2-ml. pipet whose tip was covered by a small piece of filter paper to prevent solid particles
Experimental Preparation and Purification of Trinitrotriamminecobalt(Z1Z). Co(SH3)3(K02)3was prepared as described by R0chow.j Conductivity studies revealed the pres(1) Abstracted in part from a thesis submitted by R. N. Schwartz ence of significant amounts of an ionic impurity in partial fulfillment of the requirrnents for the M.S. degree, -4ug. believed to be [ C O ( S H ~ ) ~ ( S O ~ ) ~ ] [ C O ( T \ T H ~ ) 1964. ~(~O~),].~ Repeated rt:crystallizatioris failed to reduce the con(2) W.L. Masterton and J. A. Scola. J . P h y s . Chem., 6 8 , 14 (1964). ductivity. I'urjfication was accomplished by an anion(3) F. A. Long and W. F. .McDevit, Chem. R m . . 51, 119 (1952). (4) J. N. Breinsted, A. Delbanco. and K. Volqvarts. Z . p h y s i k . Chem.. exchange tevhnique. A saturated solution of the com162, 128 (1932). plex was passed through a column containing Amberlite ( 5 ) E. G. Rochoa, Inorg. Syn., 6 , 189 (1960). IRA-400 resin in the chloride form. The impure (6) W. E. Cooley, C . F. Liu. and J. C . Bailar. J r . , J . A m . Chem. Soc., product, brought out of solution by freeze-drying, was 81, 4189 (1959). The Journal of Physical Chemistry
ACTIVITY COEFFICIENT OF
TRINITROTRIAMMINECOBALT(III)
from entering. The sample was then diluted to 25 ml. and its optical density was measured. Experience showed that saturation was achieved by shaking for 2 niin. Optical densities of solutions shaken for longer tinies were slightly higher, increasing by about 1% for every 10 min. of additional shaking. This increase is presumably due to slow aquation of the complex. The solubility in water, as determined from ten trials, was found to be 0.00811 mole/l., with an average deviation of 0.7%. The solubility of Co(SH3)3(N02)3in solutions of nine alkali halides (NaF, KaCl, SaBr, NaI, LiCl, KCl, RbCl, CsCl, and KI) was determined at salt concentrations of 0.2 and 0.4 M by the technique described above. Duplicate runs at each concentration checked within =tl%. Each tine a new salt was introduced, a check determination was made on the solubility in pure water. Direct addition of the salts to water solutions of the complex gave no change in optical density.
1547
or y/yo, increases strongly as the sizes of the alkali halide ions increase. Indeed, there is a nearly linear relationship between k , arid the suni of the crystallographic radii (u+, a-) of the ions (Figure 1). h similar relationship has been found with a few other nonelectrolytes, notably benzoic acid.7 For most nonelectrolytes, it is found that while salting-in generally increases with ionic size, the correlation is less exact. For example, salt effects for lithium chloride are frequently intermediate between those for sodiuni and potassium chlorides.
qNaF
-
Results The data for each salt can be represented, within experimental error, by the Setschenow equation log So/S
=
k,C,
(1)
where So is the solubility of the nonelectrolyte in water, S is its solubility in a salt solution of molarity C,, and IC, is a parameter characteristic of a particular salt. All of the alkali halides except sodiuni fluoride gave negative k , values, corresponding to salting-in. Table I lists Setschenow parameters derived from the solubility data; values found by Bransted are given in parentheses. The third column of the table lists the activity coefficient ratio, y / y o , at a salt concentration of 0.4 M , as calculated from the thermodynamic relation 7/70 =
So/S
(2)
I t will be observed from Table I that the extent to which C O ( N H ~ ) ~ ( NisOsalted-in, ~)~ as measured by k,
NaF
LiCl NaC1 NaBr
NaI KC1 RbCl CsCl
KI
ks
0 -0 -0 -0 -0 -0 -0 -0 -0
020 024 099 ( - 0 16) 162 236 2 5 2 ( - 0 24) 30; 372 396
( Y / Y O ) at
Cs =
1.02 0.98 0.91 0.86 0.81 0.79 0.75 0.71 0.70
1
I
I
I
I
2.50
(a+
+ a - ) , .A.
3.00
I
I
3.RO
Figure 1. Variation of k , with ionic radii
In interpreting therniodynaniic data for electrolyte solutions in which molecules or “ion pairs” are present, it is frequently assunied that the activity coefficients of these species are nearly unity. The data in Table I suggest that this approximation may lead to considerable error, at least where large inclecules are involved. The activity coefficient of CO(XH3)3( S O & in 0.40 M KI solution is approximately the same as that of pure KI ( 7 = 0.69) at this concentration.
Discussion
Table I : Setschenow Parameters and Activity Coefficients of Co(NH3)3(NO2h in Salt Solutions Salt
-0.40
0.4
Several different theories of the salt effect have been proposed. Three of these theories are examined in the following paragraphs. 1. The internal pressure concept, developed by JIcDevit and Long,8 relates salting-in or salting-out to the expansion or contraction that occurs when the (7) J. 0’11.Bockris, J. Bowler-Reed, and J. A. Kitchener, Trans. Faraday s o c . , 47, 184 (1951). (8) W. F. McDevit and F. A. Long, J . A m . Chem. SOC..74, 1773 (1952).
Volume 69, Sumher 5
Mag 1965
1548
W. L. MASTERTON AND ROBERT N.SCHRARTZ
salt is added to water. Specifically, the theory predicts that for a given nonelectrolyte k,
=
constant ( V , - V,O)
(3)
where V , is the molar volume of the liquid salt and p> its partial molar volume a t infinite dilution. For all of the alkali halides studied, the quantity ( V , - pao) is positive. This should give positive k, values, contrary to what is observed with CO(xH3)3(T\TO2)3. ;\Joreover, the salt order predicted by eq. 3 differs considerably from that found. I t would appear that the interna! pressure theory, which was developed primarily to explain salt effects with small nonpolar nonelectrolytes, cannot readily be extended to large molecules containing several polar groups. 2. Electrostatic theories consider only the electrostatic interactions between ions on the one hand and solvent or nonelectrolyte molecules on the other. ,~ be One of these approaches, due to I G r k w ~ o dshould applicable to polar as well as nonpolar nonelectrolytes. The Kirkwood theory predicts that k,
=
1 a+b
constant X
__
(4)
where a is the average of the ionic radii, a+ and a_, and b is the radius of the nonelectrolyte. For a molecule as large as C O ( N H ~ ) ~ ( ? J Owhere , ) ~ , b is about 4 A., k, should be nearly independent of the salt. For example, one can calculate that k, for potassium iodide should be only about 7% greater than k, for sodium chloride. Experimentally, it is found that the magnitude of k, is strongly dependent on the nature of the salt; the value for potassium iodide is nearly four times that for sodium chloride. An earlier electrostatic theory proposed by Debye and JlcAulay'O relates the salt effect to the change in dielectric constant brought about by dissolving the nonelectrolyte. The Debye-McAulay equation may be expressed as
k,=A
[b,- + -
a'_]
For water solutions at 25", with ionic radii in A.
A
=
0.020
Do [T-]
-
D
where Do is the dielectric constant of pure water and D the dielectric constant of a solution of the nonelectrolyte of molar concentration Ci. The Debye-RIcAulay equation predicts a greater dependence of k, on the nature of the salt than does the Kirkwood expression, since it involves the individual The Joicrnd of Physical Chemistry
radii of the ions rather than the sum of the radii of ions and nonelectrolyte molecule. If the addition of nonelectrolyte decreases the dielectric constant, as is ordinarily the case, one should observe a salting-out effect which decreases with increasing ion size. Since the salt order predicted by eq. 5 and 6 with Do > D is very similar to that found, it would appear that the data f ~ r C o ( N H ~ ) ~ ( N O ~ ) ~bec fitted o u l d by addinga constant salting-in term to the Debye-McAulay equation. 3. Some theories include the effect of dispersion as well as electrostatic forces. Although the dispersion effect is difficult to evaluate quantitatively, it can be expected to lead to salting-in of the type observed with CO("&(r\T02)3. For example, Bockris, Bowler-Reed, and Kitchener,' by considering dispersion forces, arrive a t an equation similar to that of Debye and McAulay except for the inclusion of a negative, salting-in term
where CY+ and CY- are the polarizabilities of cation and anion, respectively, and the v's are characteristic frequencies. The second term in eq. 7 is derived by considering dispersion forces between the ions on the one hand and nonelectrolyte or solvent molecules on the other. The quantity B' incorporates several parameters characteristic of the solvent and nonelectrolyte but is independent of the salt. For spherically symmetrical ions, where the polarizability is directly proportional to the ionic volume, the second term is nearly independent of the salt and one can write
Equation 8 fits the data for Co(hTH&(NO& very well. Indeed, if one adjusts the cryst,allographic radii a+ and a- for the effect of hydration by adding 0.85 and 0.10 A. for the cation and anion, respectively, as suggested by Altschuller and Everson," the salt order predicted by eq. 8 is identical with that given in Table I. One can find empirical values of A and B ( A = 1.18; B = 1.43) which reproduce the k, values within experimental error. (9) J. G . Kirkwood, E. J. Cohn, and J. T. Edsall, "Proteins, Amino Acids and Peptides," Reinhold Publishing Corp., New York, N. Y., 1943, Chapter 12. (10) P. Debye and J. McAulay; Physik. Z., 26, 22 (1925). ( 1 1 ) A. P. Altschuller and H. E. Everson, J . Phys. Chem., 55, 1368 (1951).
ACTIVITY COEFFICIENT OF
TRINITROTRIAMMINECOBALT(III)
The agreement between the observed salt effects and the predictions of the Bockris theory may be in part fortuitous. Unfortunately, the parameters necessary to evaluate A and B in eq. 8 are not available for this system and would be extremely difficult to obtain experimentally. It is clear, however, that the k, values for this system fit an equation of the form predicted by Bockris better than any other which has been proposed. An empirical equation suggested by Long and hIcDevit,3 involving a constant electrostatic term and a salt-dependent dispersion term, predicts a salt order markedly different from that observed. The same situation arises if one attempts to extend
1549
the internal pressure theory by taking into account electrostatic effects. The importance of considering dispersion forces in any treatment of salt effects with large, nonelectrolyte molecules is perhaps obvious from the data in Table I. Even with sodium fluoride, where the electrostatic effect is a maximum, the electrostatic and dispersion terms in eq. 8 are about equal in magnitude, leading to a k , value of nearly zero.
Acknowledgment. This work was supported in part by a grant from the Research Foundation of the University of Connecticut.
Volume 69,Number 6
May 1966
